Mobile stations and base stations in a mobile radio system transmit and receive digitally modulated radio frequency signals. The received signals, which have been transmitted via the mobile radio channel, are subject to linear distortion as a result of reflection, scatter and diffraction of the radio frequency signals on obstructions such as buildings or the like. The distortion may be described by the channel impulse response. In order to allow equalization of the received signal, the receiver has to know the channel impulse response of the mobile radio channel. Since the channel characteristic is changing all the time, the receiver carries out rapidly repeated channel estimates in order to determine and update the channel impulse response. For this purpose, the transmitter emits a training sequence, which is known to the receiver, in each burst. The receiver compares the received training sequence with the (known) transmitted training sequence, and determines the channel impulse response from this comparison.
The GSM (Global System for Mobile Communication) mobile radio standard and its further development (EDGE (Enhanced Data Rates for GSM Evolution) are TDMA methods (Time Division Multiple Access). Both methods use signal transmission in bursts. The structure of a GSM burst is identical to the structure of an EDGE burst, and is illustrated in FIG. 1. The burst comprises 148 symbols s0, s1, . . . , s147. The first three symbols s1, s1, s2 in the LTS (Left Tail Symbols) section are initial symbols. The following burst section LDS (Left Data Symbols) contains first data symbols s3, . . . , s60. The training sequence TS is formed by the symbols s61, . . . , s86. The RDS (Right Data Symbols) bust section contains data symbols s87, . . . , s144. The RTS (Right Tail Symbols) section at the end of the burst contains a further three symbols s145, s146, s147.
The symbols in the training sequence TS are always +1 or −1. In the case of GSM, this also applies to the other symbols, since GSM uses a two-value modulation alphabet (GMSK modulation). 8-PSK modulation (Phase Shift Keying) is defined in the EDGE Standard, whose symbol alphabet comprises eight different complex symbols. 8-PSK symbols are rotated incrementally through the angle φ=ej3π/8, while GMSK symbols are rotated incrementally through the angle φ=ejπ/2. In this case, j denotes the imaginary unit. The equalization of 8-PSK symbols is thus considerably more susceptible to channel estimation errors than equalization of GMSK symbols.
As is generally known, the mobile radio channel between a transmitter S and a receiver E can be modelled as a transmission filter H with channel coefficients hk, as is shown in FIG. 2. The transmitter S feeds transmission symbols sk into the transmission channel, that is to say the transmission filter H. A model adder SU takes account of an additive noise contribution nk, which is added to the transmission symbols sk, which have been filtered by hk, at the output of the transmission filter H.
The index k denotes the discrete time in time units of the symbol clock rate. The transmission signals sk, which have been filtered by the transmission filter H and on which noise has been superimposed, are received by the receiver E as the received signal xk. The received signal xk is obtained by convolution of the sequence of transmitted symbols with the channel impulse response plus the noise contribution:
                                          x            k                    =                                                    ∑                                  i                  =                  0                                L                            ⁢                                                h                  i                                ⁢                                  s                                      k                    -                    i                                                                        +                          n              k                                      ,                            (        1        )            where L represents the order of the transmission channel which is modelled by the filter H.
FIG. 3 shows a channel model filter H of order L. The filter H has a shift register comprising L memory cells Z. Taps (a total of L+1 of them) are in each case located in front of and behind each memory cell Z and lead to multipliers which multiply the values of the symbols sk, sk−1, . . . , sk−L inserted into the shift register via an input IN at the symbol clock rate T−1 by the corresponding L+1 channel coefficients h0, h1, . . . , hL. L+1 also denotes the length of the channel impulse response. An output stage AD of the filter H adds the outputs of the L+1 multipliers, thus resulting in an output signal OUT as shown in equation 1.
For channel estimation, it is now assumed that the receiver is synchronized to the burst limits at least sufficiently accurately that L+1 elements of the carrierh=[h−L . . . h−1h0h1 . . . hL]  (2)represent the channel impulse response. This means that the actual channel impulse response is formed by L+1 elements of this carrier, and that the other elements of the carrier are 0. If the synchronization with the burst limits is perfect, the first L channel coefficients h−L, . . . , h−1=0 and h0, h1, . . . , hL of the carrier are the channel coefficients quoted in equation 1. In order to avoid an excessively complex mathematical representation, the same notation is used for the channel coefficients that occur in equation (1) and for the elements h−L, . . . , hL of the carrier h which are mentioned in equation (2).
If the symbols of the training sequence TS are regarded as transmitted symbols, the following relationship is obtained from equation (1) in conjunction with equation(2):xk=[s61+k+L . . . s61+k . . . s61+k−L][h−L . . . h0 . . . hL]T+nk  (3)
The received symbols in the time interval [k1, k2] follow from
                              [                                                                      x                                      k                    1                                                                                                      ⋮                                                                                      x                                      k                    2                                                                                ]                =                                            [                                                                                          s                                              61                        +                                                  k                          1                                                +                        L                                                                                                  …                                                                              s                                              61                        +                                                  k                          1                                                -                        L                                                                                                                                  ⋮                                                        ⋰                                                        ⋮                                                                                                              s                                              61                        +                                                  k                          2                                                +                        L                                                                                                  ⋯                                                                              s                                              61                        +                                                  k                          2                                                -                        L                                                                                                        ]                        ⁢                                                  [                                                                                h                                          -                      L                                                                                                                    ⋮                                                                                                  h                    L                                                                        ]                    +                      [                                                                                n                                          k                      1                                                                                                                    ⋮                                                                                                  n                                          k                      2                                                                                            ]                                              (        4        )            
The abbreviation [s61 . . . s86]=[t0 . . . t25] will be used in the following text for the training symbols. The training sequence TS can be represented by the vectort=[t0 t1 t2 . . . t15 t0 . . . t9]T  (5).
The superscript T (transposed) indicates that t is a column vector. The training sequence TS thus has a periodicity with respect to a subsequence of length P. For GSM/EDGE, P=16.
Furthermore, the training sequence TS has the characteristic that each vector element of length 16 (in general: of length P)t16(1)=[t1 . . . t1+15]T  (6)is orthogonal with respect to non-trivial cyclic position shifts r in the interval tε[1, Lt]. For GSM/EDGE Lt=6, that is to sayR(1, 1+τ)=[t1, . . . , t1+15][t1+τ, . . . , t1+τ+15]T=0 for |τ|ε[1, 6].  (7)
Two approaches for estimation of the channel impulse response are known from the prior art. In the first approach, the channel impulse response is estimated using the least squares method (least square estimation: LSE) on the basis of equation (4). Equation (4) can be solved by the least squares method, since all of the elements in the matrix are known symbols from the training sequence TS. In order to avoid overdefinition of the equation system (4), the number of unknown channel coefficients [h−L . . . hL] of the carrier must be reduced to L+1 (the length of the channel impulse response). This requires more accurate synchronization, which necessitates additional complexity (it should be remembered that, before this synchronization, it is not known which of the L+1 elements of the channel impulse response carrier h represents the channel coefficients [h0 . . . hL]).
A further method which is known from the prior art for estimation of the channel impulse response is correlation of the kernel t16(5.0)=[t5 . . . t20] of the training sequence with the received symbols. The five elements on the left and the five elements on the right of the overall training sequence represent repetitions of the kernel of the training sequence. The correlation algorithm is:
                                                                                          h                  ^                                l                            =                                                                    1                    16                                    [                                                                                                              t                          5                                                                                            ⋯                                                                                              t                          20                                                                                                      ]                                ⁡                                  [                                                                                                              x                                                      5                            +                            l                                                                                                                                                              ⋮                                                                                                                                      x                                                      20                            +                            l                                                                                                                                ]                                                                                                                                                                                                                            l                =                                  -                  L                                            ,              …              ⁢                                                          ,              L                                                          (        8        )            where ĥl represent the 2L+1 estimated values for the parameters for the channel impulse response carrier h based on equation (2). The highest adjacent L+1 estimated values of the 2L+1 correlation values ĥl represent the L+1 estimated channel coefficients based on equation (1). Correlative determination of the channel coefficients thus allows the synchronization of the receiver at the same time.
According to equation (8), the correlation window runs over the received symbols, that is to say the distorted training sequence. FIG. 4 illustrates the conventional correlation process for L=6. The received burst is obtained from the superimposition of the 13 (in general: 2L+1) received burst components B−6, . . . , B0, . . . , B6, which once again result, based on equation (3), from the transmitted burst by a respective shift through one symbol time period and weighting with the channel coefficients. The box with the diagonal line represents the respective kernel of the received training sequence. This kernel is denoted by the reference symbol K for the received burst component B−6. The five data symbols, which are repetitions of a part of the kernel K, are located on each of the two sides of the kernel K. The reference symbol TS in this case denotes the training sequence of the received burst component B−6,.
The kernel of the undistorted training sequence is illustrated in the lower part of FIG. 4 for three different times (1=−6, 0, +6). Correlation of the entire received burst with the undistorted training sequence at the time 1=0 results in suppression of all the burst components transmitted via the channel except for the burst component B0 that is weighted with the channel coefficient h0. The correlation result is thus 16h0 (since the kernel has 16 symbols). The other channel coefficients are obtained by shifting the time window to the left or right.
FIG. 4 clearly shows that, when calculating h0, the correlations with the burst components B−6 and B6 each include a multiplication by an unknown data symbol (s87 and s60, respectively). The other correlation results contain a large number of multiplications of undistorted symbols in the training sequence by unknown data symbols. This is particularly evident for the correlation windows F−6 and F6 which are used for the calculation of the channel coefficients h−6 and h6. In consequence, this results in significant correlation errors.
German Laid-Open Specification DE 100 43 742 A1 disclosed a method for correlative estimation of the channel impulse response, in which the correlation window runs over the received data symbols.